Group algebras of reductive $p$-adic groups, their representations and their noncommutative geometry
Representation Theory
2025-10-21 v1 K-Theory and Homology
Abstract
This is a survey paper about representation theory and noncommutative geometry of reductive p-adic groups G. The main focus points are: 1. The structure of the Hecke algebra H(G), the Harish-Chandra-Schwartz algebra S(G) and the reduced C*-algebra . 2. The classification of irreducible G-representations in terms of supercuspidal representations. 3. The Hochschild homology and topological K-theory of these algebras. In the final part we prove one new result, namely we compute including torsion elements, in terms of equivariant K-theory of compact tori.
Cite
@article{arxiv.2510.17260,
title = {Group algebras of reductive $p$-adic groups, their representations and their noncommutative geometry},
author = {Maarten Solleveld},
journal= {arXiv preprint arXiv:2510.17260},
year = {2025}
}